Im pretty sure there is no serial number on the box of the XB360, just on the console itself. Hence they have a hole in the box showing the back of the console's serial number.

I would take it back to Comet in ya mates box.

Just remember, they maybe able to tell the difference of each console.

The Core/Arcade has a white plastic game slot (DVD draw), pro has a silver. Easiest way of telling the two apart.